Thursday, January 29, 2009

For Thought - Your High School Geometry

Remember your High School Geometry?

Remember lines? How they extend in both directions unendingly? They have length, but no width. What sort of thing is a line? What do you suppose an infinitely long line is like? Does it make sense to think or talk about an infinite line?

Now think about circles. What sort of a thing is a circle? What does it look like? If all circles look the same, how big could a circle be and still be considered a circle? What might a circle of infinite circumference look like?

Do you think you see a relationship between these two things? What is the image above a picture of?

4 comments:

Evan said...

Perhaps we were too hard on M.J. Phillips. Was that his name? My memory gets fuzzy sometimes. "Every type of thing is a thing".

B said...

Y'know, I was actually thinking about good old M.J. Philp the other day. I looked him up on teh intarwebz but couldn't locate him.

For those of you who don't know, it's a pretty funny story. The first day of college we took a class together. It was Philosophy 100 "Critical Thinking", which was taught by this older Australian gentleman in his last semester at the school.

The first thing this M.J. Philp said to the class was, "Every sort of thing is a thing." Now since that time I have come to wonder if he was describing the concept of identity, or categorization, or something else entirely, but at the time we laughed like noone's business because it seemed so absurd.

So we went to the first...week of class...maybe? After that we skipped everything until pretty much a week before the final. We became really REALLY good Spades players in the meantime.

I'm not sure if he was good-hearted or just tired of college kids. Either way, when we went to him to ask if we could still pass he told us, "You seem like smart chaps, so why don't I just give you a grade for the whole semester based on whatever you get on your final."

So we both got "A's". It definitely began a pretty major downslide in both of our educations though. I still laugh when I see it on my undergrad trascript though.

I think I will ponder over "Every sort of thing is a thing" until the day I die. Thank you M.J. Philp...whereever you are.

Pocket Size said...

Ya know, that's the hazard of being too smart. School starts to seem like a joke and you can sorta blow it off, until you get to the level where the material is smarter than you.

B said...

In a way you are right. I think the important thing is that you actually do some thinking. How you think about concepts like infinity or straight lines or circles might not be very useful in your day-to-day life, but they are good exercises for your brain in abstracting and thinking.

Finding interesting and meaningful links between seemingly different things is a valuable ability.